To use this notebook to compute line integrals, enter/edit the vector field and parametric equations marked in red.

(Note that all of the computation is done in the two blue lines,while the rest is just there to print the results nicely.)

Clear[f, F, r, v, x, y, z, t, t1, t2, Derivative, i, j, k, 
          answer];

F[x_, y_, z_] = {-1*x, y, 0};  (* vector field *)
Print[" "];
Print[" F = ", F[x, y, z][[1]], "i + ", F[x, 
              y, z][[2]], "j + ", F[x, y, 
              z][[3]], "k"];

x[t_] = t;               
y[t_] = 
        2*t;
z[t_] = 0;
t1 = 
        0;
t2 = 2;

Print["Curve:    \
x[t] = ", x[t]];
Print["          y[t] = ", 
        y[t], "           ", t1, " < t < ", 
        t2];
Print["          z[t] = ", z[t]];


r[t_] = {x[t], y[t], z[t]};

answer  = 
          Integrate[F[x[t], y[t], z[t]] . r'[t], {t, t1, t2}];
Print[" "];
Print["The line integral of F.dr is ", 
        answer];
Print[" "];

Clear[f, F, r, v, x, y, z, t, t1, t2, Derivative, i, j, k, 
          answer];

F[x_, y_, z_] = {-1*x, y, 0};  (* vector field *)
Print[" "];
Print[" F = ", F[x, y, z][[1]], "i + ", F[x, 
              y, z][[2]], "j + ", F[x, y, 
              z][[3]], "k"];

x[t_] = t;               
y[t_] = 
        t^2;
z[t_] = 0;
t1 = 
        0;
t2 = 2;

Print["Curve:    \
x[t] = ", x[t]];
Print["          y[t] = ", 
        y[t], "           ", t1, " < t < ", 
        t2];
Print["          z[t] = ", z[t]];


r[t_] = {x[t], y[t], z[t]};

answer  = 
          Integrate[F[x[t], y[t], z[t]] . r'[t], {t, t1, t2}];
Print[" "];
Print["The line integral of F.dr is ", 
        answer];
Print[" "];